Vehicle-as-Prompt: A Unified Deep Reinforcement Learning Framework for Heterogeneous Fleet Vehicle Routing Problem

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional algorithms. While serving as a primary NCO approach for solving general VRPs, current cross-problem learning paradigms are still subject to performance degradation and generalizability decay, when transferring from simple VRP variants to those involving different and complex constraints. To strengthen the paradigms, this paper offers an innovative "Multi-problem Pre-train, then Single-problem Fine-tune" framework with Federated Learning (MPSF-FL). This framework exploits the common knowledge of a federated global model to foster efficient cross-problem knowledge sharing and transfer among local models for single-problem fine-tuning. In this way, local models effectively retain common VRP knowledge from up-to-date global model, while being efficiently adapted to downstream VRPs with heterogeneous complex constraints. Experimental results demonstrate that our framework not only enhances the performance in diverse VRPs, but also improves the generalizability in unseen problems.

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and superior reasoning capabilities. In particular, autoregressive solvers integrated with reinforcement learning have emerged as a prominent trend. However, much of the existing work emphasizes large-scale generalization of neural approaches while neglecting the limited robustness of attention-based methods across heterogeneous distributions of problem parameters. Their improvements over heuristic search remain largely restricted to hand-curated, fixed-distribution benchmarks. Furthermore, these architectures tend to degrade significantly when node representations are highly similar or when tasks involve long decision horizons. To address the aforementioned limitations, we propose a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems and generate a constraint assignment matrix. This matrix is subsequently integrated adaptively into the feature representation learning and decision process of the autoregressive solver, serving as a graph structure mask that facilitates the formation of solutions characterized by both global vision and local feature integration. To the best of our knowledge, this work represents the first comprehensive experimental investigation of neural network model solvers across a 378-combinatorial space spanning four distinct dimensions within the CVRPlib public dataset. Extensive experimental evaluations demonstrate that our proposed fusion model effectively captures and leverages problem constraints, achieving state-of-the-art performance across multiple benchmark datasets.

Solving practical multi-depot vehicle routing problems (MDVRP) is a challenging optimization task central to modern logistics, increasingly driven by e-commerce. To address the MDVRP's computational complexity, neural-based combinatorial optimization methods offer a promising scalable alternative to traditional approaches. However, neural-based methods typically rely on rigid architectures and input encodings tailored to specific problem formulations. In real-world settings, heterogeneous constraints create multiple MDVRP variants, limiting the applicability of such models. While multi-task learning (MTL) has begun to accelerate the development of unified neural-based solvers, prior works focus almost exclusively on single-depot VRPs, leaving the MDVRP unaddressed. To bridge this gap, we propose Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing (FiLMMeD), a novel unified neural-based model for 24 different MDVRP variants. We introduce three main contributions: (1) to improve the model's generalization, we augment the standard Transformer encoder with Feature-wise Linear Modulation (FiLM), which dynamically conditions learned internal representations based on the active set of constraints; (2) we provide an initial demonstration of Preference Optimization in the MTL setting, establishing it as a superior alternative to Reinforcement Learning for future MTL works; (3) to mitigate the generalization gap caused by the introduction of multi-depot constraints, we introduce a targeted curriculum learning strategy that progressively exposes the model to increasingly more complex constraint interactions. Extensive experiments on 24 MDVRP variants (including 8 novel formulations) and 16 single-depot VRPs confirm the effectiveness of FiLMMeD, which consistently outperforms state-of-the-art baselines. Our code is available at: https://github.com/AJ-Correa/FiLMMeD/tree/main